# LINR 1| Lesson 1| Practice Key

Table 1

Complete each section to show your understanding for linear patterns.

## Tables

The following tables represent linear patterns. The tables and graphs are created using Desmos.com.

1. Find the missing values in each table. Table 1: (3, 7) and (12,15); Table 2: (4, 9) and (21, -42); Table 3: (-2, 4) and (8, 24)
2. Graph each table on a coordinate plane.
3. Calculate the slope using the table. Table 1: change in $$y$$ is 4 and change in $$x$$ is 1, i.e. slope is 4; Table 2: change in $$y$$ is -3 and change in $$x$$ is 1, i.e. slope is -3; Table 3: change in $$y$$ is 2 and change in $$x$$ is 1, i.e. slope is 2.
4. Calculate the slope using the graph.
5. Determine the point of the $$y$$ intercept. Table 1:
6. Write an equation to determine the $$y$$value given any $$x$$-value. Table 1 equation: $$y = 4x -5$$; Table 2 equation: $$y=21 – 3x$$; Table 3 equation: $$y= 2x + 8$$

## Patterns

Given the growth pattern shown in Figure 2 and Figure 4.

1. Draw Figure 3. Figure 3 has 3 rows of 6, so a row of 6 is added to figure2.
2. Explain the growth pattern. 6 is added each time.
3. Determine the number of squares in Figure 0. Figure 0 has 1 square.
4. Write the equation to represent the number of squares for any figure. 1 + 6n, where n is the figure number.
5. Using the context of growth patterns, explain why $$m$$ represents the slope and $$b$$ represents the $$y$$-intercept in the slope-intercept formula $$y=mx+b$$. The slope is 6 since, 6 squares is added each time and 1 is figure 0, so the $$y$$-intercept

A given linear pattern has 10 squares in Step 3.  The pattern grows by -4 squares every 2 steps.

1. Create a table for this pattern.
2. Calculate the slope to represent the growth for this pattern. Slope is -4
3. Calculate the equation to calculate the number of squares for each step. $$y = 22 – 4x$$